Never mind the drones - they will be produced by colonies which may then swarm later - due to one or more of several reasons.
Last year, most beeks were pulling their hair out at the length of time taken for the queens to get mated as the weather was not particularly conducive for the most part of May. Some were reporting unprecedented (well undocumented) times before queens finally came into lay and many were disappointed (queens not mated). This was after a particularly warm and mild April when all and sundry either made splits or had to A/S.
Sooo, if you can predict the weather, you will know when you can start.
Your planned methodology is flawed. Do not expect good queens from Q- hives - they may be OK, but are often less than optimal. You need to produce queen cells from very strong colonies, preferably few of them, for the best results.
Certainly with only four frames of brood in a deep brood is far too early to be considering splitting - they are not even yet ready for supering.
I would suggest you select the colony(ies) from which you would prefer to raise queens from; they may not be your ones in deeps. After choosing your time, demaree those hives and use the queen cells produced, under the supercedure instinct, for transferring to your splits.
RAB